Essays: Scientific, Political, and Speculative, Volume I

"However, spite of these difficulties, the current hypothesis is, that the Sun and planets, inclusive of the Earth, are either solid or liquid, or have solid crusts with liquid nuclei."23

After saying that the familiarity of this hypothesis must not delude us into uncritical acceptance of it, but that if any other hypothesis is physically possible it may reasonably be entertained, it was argued that by tracing out the process of condensation in a nebulous spheroid, we are led to infer the eventual formation of a molten shell with a nucleus consisting of gaseous matter at high tension. The paragraph which then follows runs thus: —

"But what," it may be asked, "will become of this gaseous nucleus when exposed to the enormous gravitative pressure of a shell some thousands of miles thick? How can aeriform matter withstand such a pressure?" Very readily. It has been proved that, even when the heat generated by compression is allowed to escape, some gases remain uncondensible by any force we can produce. An unsuccessful attempt lately made in Vienna to liquify oxygen, clearly shows this enormous resistance. The steel piston employed was literally shortened by the pressure used; and yet the gas remained unliquified! If, then, the expansive force is thus immense when the heat evolved is dissipated, what must it be when that heat is in great measure detained, as in the case we are considering? Indeed the experiences of M. Cagniard de Latour have shown that gases may, under pressure, acquire the density of liquids while retaining the aeriform state, provided the temperature continues extremely high. In such a case, every addition to the heat is an addition to the repulsive power of the atoms: the increased pressure itself generates an increased ability to resist; and this remains true to whatever extent the compression is carried. Indeed it is a corollary from the persistence of force that if, under increasing pressure, a gas retains all the heat evolved, its resisting force is absolutely unlimited. Hence the internal planetary structure we have described is as physically stable a one as that commonly assumed."

Had this paragraph, and the subsequent paragraphs, been written five years later, when Prof. Andrews had published an account of his researches, the propositions they contain, while rendered more specific and at the same time more defensible, would perhaps have been freed from the erroneous implication that the internal structure indicated is an universal one. Let us, while guided by Prof. Andrews' results, consider what would probably be the successive changes in a condensing nebulous spheroid.

Prof. Andrews has shown that for each kind of gaseous matter there is a temperature above which no amount of pressure can cause liquefaction. The remark, made a priori in the above extract, "that if, under increasing pressure, a gas retains all the heat evolved, its resisting force is absolutely unlimited", harmonizes with the inductively-reached result that if the temperature is not lowered to its "critical point" a gas does not liquify, however great the force applied. At the same time Prof. Andrews' experiments imply that, supposing the temperature to be lowered to the point at which liquefaction becomes possible, then liquefaction will take place where there is first reached the required pressure. What are the corollaries in relation to concentrating nebulous spheroids?

Assume a spheroid of such size as will form one of the inferior planets, and consisting externally of a voluminous, cloudy atmosphere composed of the less condensible elements, and internally of metallic gases: such internal gases being kept by convection-currents at temperatures not very widely differing. And assume that continuous radiation has brought the internal mass of metallic gases down to the critical point of the most condensible. May we not say that there is a size of the spheroid such that the pressure will not be great enough to produce liquefaction at any other place than the centre? or, in other words, that in the process of decreasing temperature and increasing pressure, the centre will be the place at which the combined conditions of pressure and temperature will be first reached? If so, liquefaction, commencing at the centre, will spread thence to the periphery; and, in virtue of the law that solids have higher melting points under pressure than when free, it may be that solidification will similarly, at a later stage, begin at the centre and progress outwards: eventually producing, in that case, a state such as Sir William Thomson alleges exists in the Earth. But now suppose that instead of such a spheroid, we assume one of, say, twenty or thirty times the mass; what will then happen? Notwithstanding convection-currents, the temperature at the centre must always be higher than elsewhere; and in the process of cooling the "critical point" of temperature will sooner be reached in the outer parts. Though the requisite pressure will not exist near the surface, there is evidently, in a large spheroid, a depth below the surface at which the pressure will be great enough, if the temperature is sufficiently low. Hence it is inferable that somewhere between centre and surface in the supposed larger spheroid, there will arise that state described by Prof. Andrews, in which "flickering striæ" of liquid float in gaseous matter of equal density. And it may be inferred that gradually, as the process goes on, these striæ will become more abundant while the gaseous interspaces diminish; until, eventually, the liquid becomes continuous. Thus there will result a molten shell containing a gaseous nucleus equally dense with itself at their surface of contact and more dense at the centre – a molten shell which will slowly thicken by additions to both exterior and interior.

That a solid crust will eventually form on this molten shell may be reasonably concluded. To the demurrer that solidification cannot commence at the surface, because the solids formed would sink, there are two replies. The first is that various metals expand while solidifying, and therefore would float. The second is that since the envelope of the supposed spheroid would consist of the gases and non-metallic elements, compounds of these with the metals and with one another would continually accumulate on the molten shell; and the crust, consisting of oxides, chlorides, sulphurets, and the rest, having much less specific gravity than the molten shell, would be readily supported by it.

Clearly a planet thus constituted would be in an unstable state. Always it would remain liable to a catastrophe resulting from change in its gaseous nucleus. If, under some condition of pressure and temperature eventually reached, the components of this suddenly entered into one of those proto-chemical combinations forming a new element, there might result an explosion capable of shattering the entire planet, and propelling its fragments in all directions with high velocities. If the hypothetical planet between Jupiter and Mars was intermediate in size as in position, it would apparently fulfil the conditions under which such a catastrophe might occur.

Note IV. The argument set forth in the foregoing note, is in part designed to introduce a question which seems to require re-consideration – the origin of the minor planets or planetoids. The hypothesis of Olbers, as propounded by him, implied that the disruption of the assumed planet between Mars and Jupiter had taken place at no very remote period in the past; and this implication was shown to be inadmissible by the discovery that there exists no such point of intersection of the orbits of the planetoids as the hypothesis requires. The inquiry whether, in the past, there was any nearer approach to a point of intersection than at present, having resulted in a negative, it is held that the hypothesis must be abandoned. It is, however, admitted that the mutual perturbations of the planetoids themselves would suffice, in the course of some millions of years, to destroy all traces of a place of intersection of their orbits, if it once existed. But if this be admitted why need the hypothesis be abandoned? Given such duration of the Solar System as is currently assumed, there seems no reason why lapse of a few millions of years should present any difficulty. The explosion may as well have taken place ten million years ago as at any more recent period. And whoever grants this must grant that the probability of the hypothesis has to be estimated from other data.

As a preliminary to closer consideration, let us ask what may be inferred from the rate of discovery of the planetoids, and from the sizes of those most recently discovered. In 1878, Prof. Newcomb, arguing that "the preponderance of evidence is on the side of the number and magnitude being limited", says that "the newly discovered ones" "do not seem, on the average, to be materially smaller than those which were discovered ten years ago"; and further that "the new ones will probably be found to grow decidedly rare before another hundred are discovered". Now, inspection of the tables contained in the just-published fourth edition of Chambers' Descriptive Astronomy (vol. I) shows that whereas the planetoids discovered in 1868 (the year Prof. Newcomb singles out for comparison) have an average magnitude of 11∙56 those discovered last year (1888) have an average magnitude of 12∙43. Further, it is observable that though more than ninety have been discovered since Prof. Newcomb wrote, they have by no means become rare: the year 1888 having added ten to the list, and having therefore maintained the average rate of the preceding ten years. If, then, the indications Prof. Newcomb names, had they arisen, would have implied a limitation of the number, these opposite indications imply that the number is unlimited. The reasonable conclusion appears to be that these minor planets are to be counted not by hundreds but by thousands; that more powerful telescopes will go on revealing still smaller ones; and that additions to the list will cease only when the smallness ends in invisibility.

Commencing now to scrutinize the two hypotheses respecting the genesis of these multitudinous bodies, I may first remark concerning that of Laplace, that he might possibly not have propounded it had he known that instead of four such bodies there are hundreds, if not thousands. The supposition that they resulted from the breaking up of a nebulous ring into numerous small portions, instead of its collapse into one mass, might not, in such case, have seemed to him so probable. It would have appeared still less probable had he been aware of all that has since been discovered concerning the wide differences of the orbits in size, their various and often great eccentricities, and their various and often great inclinations. Let us look at these and other incongruous traits of them.

(1.) Between the greatest and least mean distances of the planetoids there is a space of 200 millions of miles; so that the whole of the Earth's orbit might be placed between the limits of the zone occupied, and leave 7 millions of miles on either side: add to which that the widest excursions of the planetoids occupy a zone of 270 millions of miles. Had the rings from which Mercury, Venus, and the Earth were formed been one-sixth of the smaller width or one-ninth of the greater, they would have united: there would have been no nebulous rings at all, but a continuous disk. Nay more, since one of the planetoids trenches upon the orbit of Mars, it follows that the nebulous ring out of which the planetoids were formed must have overlapped that out of which Mars was formed. How do these implications consist with the nebular hypothesis? (2.) The tacit assumption usually made is that the different parts of a nebulous ring have the same angular velocities. Though this assumption may not be strictly true, yet it seems scarcely likely that it is so widely untrue as it would be had the inner part of the ring an angular velocity nearly thrice that of the outer. Yet this is implied. While the period of Thule is 8.8 years, the period of Medusa is 3·1 years. (3.) The eccentricity of Jupiter's orbit is 0·04816, and the eccentricity of Mars' orbit is 0·09311. Estimated by groups of the first found and last found of the planetoids, the average eccentricity of the assemblage is about three times that of Jupiter and more than one and a half times that of Mars; and among the members of the assemblage themselves, some have an eccentricity thirty-five times that of others. How came this nebulous zone, out of which it is supposed the planetoids arose, to have originated eccentricities so divergent from one another as well as from those of the neighbouring planets? (4.) A like question may be asked respecting the inclinations of the orbits. The average inclination of the planetoid-orbits is four times the inclination of Mars' orbit and six times the inclination of Jupiter's orbit; and among the planetoid-orbits themselves the inclinations of some are fifty times those of others. How are all these differences to be accounted for on the hypothesis of genesis from a nebulous ring? (5.) Much greater becomes the difficulty on inquiring how these extremely unlike eccentricities and inclinations came to co-exist before the parts of the nebulous ring separated, and how they survived after the separation. Were all the great eccentricities displayed by the outermost members of the group, and the small by the innermost members, and were the inclinations so distributed that the orbits having much belonged to one part of the group, and those having little to another part of the group; the difficulty of explanation might not be insuperable. But the arrangement is by no means this. The orbits are, to use an expressive word, miscellaneously jumbled. Hence, if we go back to the nebulous ring, there presents itself the question, – How came each planetoid-forming portion of nebulous matter, when it gathered itself together and separated, to have a motion round the Sun differing so much from the motions of its neighbours in eccentricity and inclination? And there presents itself the further question, – How, during the time when it was concentrating into a planetoid, did it manage to jostle its way through all the differently-moving like masses of nebulous matter, and yet to preserve its individuality? Answers to these questions are, it seems to me, not even imaginable.

Turn we now to the alternative hypothesis. During revision of the foregoing essay, in preparation for that edition of the volume containing it which was published in 1883, there occurred the thought that some light on the origin of the planetoids ought to be obtained by study of their distributions and movements. If, as Olbers supposed, they resulted from the bursting of a planet once revolving in the region they occupy, the implications are: – first, that the fragments must be most abundant in the space immediately about the original orbit, and less abundant far away from it; second, that the large fragments must be relatively few, while of smaller fragments the numbers will increase as the sizes decrease; third, that as some among the smaller fragments will be propelled further than any of the larger, the widest deviations in mean distance from the mean distance of the original planet, will be presented by the smallest members of the assemblage; and fourth, that the orbits differing most from the rest in eccentricity and in inclination, will be among those of these smallest members. In the fourth edition of Chambers's Handbook of Descriptive and Practical Astronomy (the first volume of which has just been issued) there is a list of the elements (extracted and adapted from the Berliner Astronomisches Jahrbuch for 1890) of all the small planets (281 in number) which had been discovered up to the end of 1888. The apparent brightness, as expressed in equivalent star-magnitudes, is the only index we have to the probable comparative sizes of by far the largest number of the planetoids: the exceptions being among those first discovered. Thus much premised, let us take the above points in order. (1) There is a region lying between 2·50 and 2·80 (in terms of the Earth's mean distance from the Sun) where the planetoids are found in maximum abundance. The mean between these extremes, 2·65, is nearly the same as the average of the distances of the four largest and earliest-known of these bodies, which amounts to 2·64. May we not say that the thick clustering about this distance (which is, however, rather less than that assigned for the original planet by Bode's empirical law), in contrast with the wide scattering of the comparatively few whose distances are little more than 2 or exceed 3, is a fact in accordance with the hypothesis in question?24 (2) Any table which gives the apparent magnitudes of the planetoids, shows at once how much the number of the smaller members of the assemblage exceeds that of those which are comparatively large; and every succeeding year has emphasized this contrast more strongly. Only one of them (Vesta) exceeds in brightness the seventh star-magnitude, while one other (Ceres) is between the seventh and eighth, and a third (Pallas) is above the eighth; but between the eighth and ninth there are six; between the ninth and tenth, twenty; between the tenth and eleventh, fifty-five; below the eleventh a much larger number is known, and the number existing is probably far greater, – a conclusion we cannot doubt when the difficulty of finding the very faint members of the family, visible only in the largest telescopes, is considered. (3) Kindred evidence is furnished if we broadly contrast their mean distances. Out of the 13 largest planetoids whose apparent brightnesses exceed that of a star of the 9·5 magnitude, there is not one having a mean distance that exceeds 3. Of those having magnitudes at least 9·5 and smaller than 10, there are 15; and of these one only has a mean distance greater than 3. Of those between 10 and 10·5 there are 17; and of these also there is one exceeding 3 in mean distance. In the next group there are 37, and of these 5 have this great mean distance. The next group, 48, contains 12 such; the next, 47, contains 13 such. Of those of the twelfth magnitude and fainter, 72 planetoids have been discovered, and of those of them of which the orbits have been computed, no fewer than 23 have a mean distance exceeding 3 in terms of the Earth's. It is evident from this how comparatively erratic are the fainter members of the extensive family with which we are dealing. (4) To illustrate the next point, it may be noted that among the planetoids whose sizes have been approximately measured, the orbits of the two largest, Vesta and Ceres, have eccentricities falling between .05 and .10, whilst the orbits of the two smallest, Menippe and Eva, have eccentricities falling between .20 and .25, and between .30 and .35. And then among those more recently discovered, having diameters so small that measurement of them has not been practicable, come the extremely erratic ones, – Hilda and Thule, which have mean distances of 3.97 and 4.25 respectively; Æthra, having an orbit so eccentric that it cuts the orbit of Mars; and Medusa, which has the smallest mean distance from the Sun of any. (5) If the average eccentricities of the orbits of the planetoids grouped according to their decreasing sizes are compared, no very definite results are disclosed, excepting this, that the eight Polyhymnia, Atalanta, Eurydice, Æthra, Eva, Andromache, Istria, and Eudora, which have the greatest eccentricities (falling between .30 and .38), are all among those of smallest star-magnitudes. Nor when we consider the inclinations of the orbits do we meet with obvious verifications; since the proportion of highly-inclined orbits among the smaller planetoids does not appear to be greater than among the others. But consideration shows that there are two ways in which these last comparisons are vitiated. One is that the inclinations are measured from the plane of the ecliptic, instead of being measured from the plane of the orbit of the hypothetical planet. The other, and more important one, is that the search for planetoids has naturally been carried on in that comparatively narrow zone within which most of their orbits fall; and that, consequently, those having the most highly-inclined orbits are the least likely to have been detected, especially if they are at the same time among the smallest. Moreover, considering the general relation between the inclination of planetoid orbits and their eccentricities, it is probable that among the orbits of these undetected planetoids are many of the most eccentric. But while recognizing the incompleteness of the evidence, it seems to me that it goes far to justify the hypothesis of Olbers, and is quite incongruous with that of Laplace. And as having the same meanings let me not omit the remarkable fact concerning the planetoids discovered by D'Arrest, that "if their orbits are figured under the form of material rings, these rings will be found so entangled, that it would be possible, by means of one among them taken at hazard, to lift up all the rest," – a fact incongruous with Laplace's hypothesis, which implies an approximate concentricity, but quite congruous with the hypothesis of an exploded planet.

Next to be considered come phenomena, the bearings of which on the question before us are scarcely considered – I mean those presented by meteors and shooting stars. The natures and distributions of these harmonize with the hypothesis of an exploded planet, and I think with no other hypothesis. The theory of volcanic origin, joined with the remark that the Sun emits jets which might propel them with adequate velocities, seems quite untenable. Such meteoric bodies as have descended to us, forbid absolutely the supposition of solar origin. Nor can they rationally be ascribed to planetary volcanoes. Even were their mineral characters appropriate, which many of them are not (for volcanoes do not eject iron), no planetary volcanoes could propel them with anything like the implied velocity – could no more withstand the tremendous force to be assumed, than could a card-board gun the force behind a rifle bullet. But that their mineral characters, various as they are, harmonize with the supposition that they were derived from the crust of a planet is manifest; and that the bursting of a planet might give to them, and to shooting stars, the needful velocities, is a reasonable conclusion. Along with those larger fragments of the crust constituting the known planetoids, varying from some 200 miles in diameter to little over a dozen, there would be sent out still more multitudinous portions of the crust, decreasing in size as they increased in number. And while there would thus result such masses as occasionally fall through the Earth's atmosphere to its surface, there would, in an accompanying process, be an adequate cause for the myriads of far smaller masses which, as shooting stars, are dissipated in passing through the Earth's atmosphere. Let us figure to ourselves, as well as we may, the process of explosion.

Assume that the diameter of the missing planet was 20,000 miles; that its solid crust was a thousand miles thick; that under this came a shell of molten metallic matter which was another thousand miles thick; and that the space, 16,000 miles in diameter, within this, was occupied by the equally dense mass of gases above the "critical point", which, entering into a proto-chemical combination, caused the destroying explosion. The primary fissures in the crust must have been far apart – probably averaging distances between them as great as the thickness of the crust. Supposing them approximately equidistant, there would, in the equatorial periphery, be between 60 and 70 fissures. By the time the primary fragments thus separated had been heaved a mile outwards, the fissures formed would severally have, at the surface, a width of 170 odd yards. Of course these great masses, as soon as they moved, would themselves begin to fall in pieces; especially at their bounding surfaces. But passing over the resulting complications, we see that when the masses had been propelled 10 miles outwards, the fissures between them would be each a mile wide. Notwithstanding the enormous forces at work, an appreciable interval would elapse before these vast portions of the crust could be put in motion with any considerable velocities. Perhaps the estimate will be under the mark if we assume that it took 10 seconds to propel them through the first mile, and that, by implication, at the end of 20 seconds they had travelled 4 miles, and at the end of 30 seconds 9 miles. Supposing this granted, let us ask what would be taking place in each intervening fissure a thousand miles deep, which, in the space of half a minute, had opened out to nearly a mile wide, and in the subsequent half minute to a chasm approaching 3 miles in width. There would first be propelled through it enormous jets of the molten metals composing the internal liquid shell; and these would part into relatively small masses as they were shot into space. Presently, as the chasm opened to some miles in width, the molten metals would begin to be followed by the equally dense gaseous matter behind, and the two would rush out together. Soon the gases, predominating, would carry with them the portions of the liquid shell continually collapsing; until the blast became one filled with millions of small masses, billions of smaller masses, and trillions of drops. These would be driven into space in a stream, the emission of which would continue for many seconds or even several minutes. Remembering the rate of motion of the jets emitted from the solar surface, and supposing that the blasts produced by this explosion reached only one-tenth of that rate, these myriads of small masses and drops would be propelled with planetary velocities, and in approximately the same direction. I say approximately, because they would be made to deviate somewhat by the friction and irregularities of the chasm passed through, and also by the rotation of the planet. Observe, however, that though they would all have immense velocities, their velocities would not be equal. During its earlier stages the blast would be considerably retarded by the resistance which the sides of its channel offered. When this became relatively small the velocity of the blast would reach its maximum; from which it would decline when the space for emission became very wide, and the pressure behind consequently less. Hence these almost infinitely numerous particles of planet-spray, as we might call it, as well as those formed by the condensation of the metallic vapours accompanying them, would forthwith begin to part company: some going rapidly in advance, and others falling behind; until the stream of them, perpetually elongating, formed an orbit round the Sun, or rather an assemblage of innumerable orbits, separating widely at aphelion and perihelion, but approximating midway, where they might fall within a space of, say, some two millions of miles, as do the orbits of the November meteors. At a later stage of the explosion, when the large masses, having moved far outwards, had also fallen to pieces of every size, from that of Vesta to that of an aerolite, and when the channels just described had ceased to exist, the contents of the planet would disperse themselves with lower velocities and without any unity of direction. Hence we see causes alike for the streams of shooting stars, for the solitary shooting stars visible to the naked eye, and for the telescopic shooting stars a score times more numerous.